Finite Group Databasebeta

← #13074331

Subgroups — #13074331

Order 1408.

1134 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 1134 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊D11C211yesmaximal, characteristic, complemented
2C2×#67006C211yesmaximal, characteristic, complemented
3C2×#66939C211yesmaximal, characteristic, complemented
4C2×#66935C211yesmaximal, characteristic, complemented
5C11×#379C211yesmaximal, characteristic, complemented
6#10622574C214yesmaximal, complemented
7#10622573C214yesmaximal, complemented
8#10622568C211yesmaximal, characteristic, complemented
9#10622556C211yesmaximal, characteristic, complemented
10C25×C11C2211yescharacteristic
11C24×D11C2211yescharacteristic
12C22×C22⋊D11—24no—
13C22×C22⋊D11—24no—
14C22×C22⋊D11—24no—
15C22×C22⋊D11C2211yescharacteristic
16C22×C22⋊D11C2214yes—
17C22×C22⋊D11C2212yescomplemented
18C23×Dic11C2211yescharacteristic
19C22×D44C2212yescomplemented
20C2×C11×C22⋊C4C2211yescharacteristic
21C2×C11×C22⋊C4C2211yescharacteristic
22C2×C11×C22⋊C4C2214yescomplemented
23#67006—24no—
24C2×C22⋊Dic11C2211yescharacteristic
25C2×C22⋊Dic11C2212yescomplemented
26C2×(C2×D11)⋊C4C2212yescomplemented
27C2×(C2×D11)⋊C4C2212yescomplemented
28C2×(C2×D11)⋊C4C2214yescomplemented
29C2×C4⋊Dic11C2212yescomplemented
30#66939—24no—
31#66935—24no—
32C11⋊#95C2214yescomplemented
33C24×C11—22no—
34C24×C11—22no—
35C24×C11—44no—
36C24×C11D414yescomplemented
37C24×C11C2312yes—
38C24×C11C2311yescharacteristic
39C23×D11—22no—
40C23×D11—22no—
41C23×D11—44no—
42C23×D11D414yescomplemented
43C23×D11C2311yescharacteristic
44C23×D11C2312yes—
45C22×C4×C11C2312yes—
46C22×C4×C11C2312yes—
47C2×C22⋊D11—232no—
48C2×C22⋊D11—28no—
49C2×C22⋊D11—28no—
50C2×C22⋊D11—22no—
51C2×C22⋊D11—22no—
52C2×C22⋊D11—22no—
53C2×C22⋊D11—24no—
54C2×C22⋊D11—28no—
55C2×C22⋊D11—44no—
56C22×Dic11—22no—
57C22×Dic11—22no—
58C22×Dic11D414yescomplemented
59C22×Dic11C2312yes—
60C22×Dic11C2311yescharacteristic
61C22×Dic11C2312yes—
62C2×D44—24no—
63C2×D44—44no—
64C11×C22⋊C4—22no—
65C11×C22⋊C4—22no—
66C11×C22⋊C4—44no—
67C22⋊Dic11—22no—
68C22⋊Dic11—24no—
69(C2×D11)⋊C4—24no—
70(C2×D11)⋊C4—24no—
71(C2×D11)⋊C4—44no—
72C4⋊Dic11—24no—
73#2613—111nomaximal, Sylow
74C23×C11—24no—
75C23×C11—28no—
76C23×C11—22no—
77C23×C11—22no—
78C23×C11—24no—
79C23×C11—24no—
80C23×C11—48no—
81C23×C11—48no—
82C23×C11—48no—
83C23×C11C2×D414yes—
84C23×C11C2×D412yes—
85C23×C11C2×D412yes—
86C23×C11C2×D412yes—
87C23×C11C2411yescharacteristic
88C22×D11—28no—
89C22×D11—22no—
90C22×D11—22no—
91C22×D11—24no—
92C22×D11—24no—
93C22×D11—21no—
94C22×D11—21no—
95C22×D11—21no—
96C22×D11—24no—
97C22×D11—48no—
98C22×D11—48no—
99C22×D11—48no—
100C22×D11C2×D414yes—
101C2×C4×C11—22no—
102C2×C4×C11—22no—
103C2×C4×C11—24no—
104C2×C4×C11—24no—
105C22⋊D11—232no—
106C22⋊D11—48no—
107C22⋊D11—44no—
108C2×Dic11—28no—
109C2×Dic11—22no—
110C2×Dic11—22no—
111C2×Dic11—21no—
112C2×Dic11—21no—
113C2×Dic11—21no—
114C2×Dic11—22no—
115C2×Dic11—24no—
116C2×Dic11C2×D414yes—
117D44—48no—
118C23×D4—111no—
119C2×#123—111no—
120C2×#120—111no—
121C2×#120—111no—
122#394—114no—
123#392—114no—
124#381—111no—
125#379—111no—
126#379D1111yescharacteristic, complemented
127C22×C11—24no—
128C22×C11—24no—
129C22×C11—24no—
130C22×C11—24no—
131C22×C11—24no—
132C22×C11—24no—
133C22×C11—416no—
134C22×C11—44no—
135C22×C11—44no—
136C22×C11#12014yes—
137C22×C11C22×D411yescharacteristic
138C22×C11C22×D411yescharacteristic
139C22×C11C22×D411yescharacteristic
140C22×C11H(5,𝔽2)14yes—
141C2×D11—24no—
142C2×D11—24no—
143C2×D11—24no—
144C2×D11—416no—
145C2×D11—44no—
146C2×D11—44no—
147C2×D11—41no—
148C2×D11—42no—
149C2×D11—42no—
150C2×D11—42no—
151C4×C11—42no—
152C4×C11—42no—
153Dic11—24no—
154Dic11—41no—
155Dic11—42no—
156C25—111no—
157C25C2×D1111yescharacteristic
158C22×D4—111no—
159C22×D4—114no—
160C22×D4—112no—
161C22×D4—112no—
162C22×D4—224no—
163C22×D4—224no—
164C22×D4—224no—
165C23×C4—111no—
166#123—224no—
167#120—224no—
168#120—224no—
169C2×C4⋊C4—112no—
170C2×C22⋊C4—111no—
171C2×C22⋊C4—112no—
172C2×C22⋊C4—112no—
173C2×C22⋊C4—112no—
174C2×C22⋊C4—114no—
175C2×C22⋊C4C2×D1111yescharacteristic
176C2×C22⋊C4C2×D1111yescharacteristic
177C2×C22⋊C4C2×D1114yescomplemented
178#95—114no—
179C2×C11—24no—
180C2×C11—44no—
181C2×C11C2×#12011yescharacteristic
182C2×C11#53412yes—
183C2×C11#53412yes—
184C2×C11#53512yes—
185D11—44no—
186D11—81no—
187C24—22no—
188C24—22no—
189C24—44no—
190C24—112no—
191C24—114no—
192C24—111no—
193C24—222no—
194C24—222no—
195C24—444no—
196C24D4414yescomplemented
197C24C22×D1112yes—
198C24C22×D1111yescharacteristic
199C2×D4—224no—
200C2×D4—228no—
201C2×D4—228no—
202C2×D4—2232no—
203C2×D4—228no—
204C2×D4—224no—
205C2×D4—222no—
206C2×D4—222no—
207C2×D4—222no—
208C2×D4—444no—
209C2×D4—444no—
210C22×C4—114no—
211C22×C4—112no—
212C22×C4—112no—
213C22×C4—111no—
214C22×C4—222no—
215C22×C4—222no—
216C22×C4C22×D1112yes—
217C22×C4C22×D1112yes—
218C4⋊C4—224no—
219C22⋊C4—22no—
220C22⋊C4—22no—
221C22⋊C4—44no—
222C22⋊C4—224no—
223C22⋊C4—224no—
224C22⋊C4—224no—
225C22⋊C4—222no—
226C22⋊C4—444no—
227C11#261311yescharacteristic, complemented, Sylow
228C23—24no—
229C23—28no—
230C23—22no—
231C23—22no—
232C23—24no—
233C23—24no—
234C23—48no—
235C23—48no—
236C23—48no—
237C23—114no—
238C23—228no—
239C23—222no—
240C23—222no—
241C23—224no—
242C23—224no—
243C23—221no—
244C23—221no—
245C23—221no—
246C23—224no—
247C23—448no—
248C23—448no—
249C23—448no—
250C23C2×D4414yes—
251C23C2×D4412yes—
252C23D4×D1112yes—
253C23D4×D1112yes—
254C23C23×D1111yescharacteristic
255D4—2232no—
256D4—448no—
257D4—448no—
258D4—444no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—24no—
262C2×C4—24no—
263C2×C4—114no—
264C2×C4—228no—
265C2×C4—222no—
266C2×C4—222no—
267C2×C4—221no—
268C2×C4—222no—
269C2×C4—221no—
270C2×C4—221no—
271C2×C4—224no—
272C22—24no—
273C22—24no—
274C22—24no—
275C22—24no—
276C22—24no—
277C22—24no—
278C22—416no—
279C22—44no—
280C22—44no—
281C22—224no—
282C22—224no—
283C22—224no—
284C22—4416no—
285C22—444no—
286C22—444no—
287C22—441no—
288C22—442no—
289C22—442no—
290C22—442no—
291C22#6693514yes—
292C22C22×D4411yescharacteristic
293C22C2×D4×D1111yescharacteristic
294C22C2×D4×D1111yescharacteristic
295C22#6703714yes—
296C4—42no—
297C4—42no—
298C4—224no—
299C4—441no—
300C4—442no—
301C2—24no—
302C2—44no—
303C2—444no—
304C2—881no—
305C2C2×#6693511yescharacteristic
306C2#1062302412yes—
307C2#1062312012yes—
308C2#1062312312yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#379C2
hypercenter#379D11
hypocenterC11#2613
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #379

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C23×C22⋊D11C2semidirect
2. C2×#67006C2semidirect
3. C2×#66939C2semidirect
4. C2×#66935C2semidirect
5. C11×#379C2semidirect
6. #10622574C2semidirect
7. #10622573C2semidirect
8. #10622568C2semidirect
9. #10622556C2semidirect
17. C22×C22⋊D11C22semidirect
19. C22×D44C22semidirect
22. C2×C11×C22⋊C4C22semidirect
25. C2×C22⋊Dic11C22semidirect
26. C2×(C2×D11)⋊C4C22semidirect
27. C2×(C2×D11)⋊C4C22semidirect
28. C2×(C2×D11)⋊C4C22semidirect
29. C2×C4⋊Dic11C22semidirect
32. C11⋊#95C22semidirect
36. C24×C11D4semidirect
42. C23×D11D4semidirect
58. C22×Dic11D4semidirect
126. #379D11semidirect
177. C2×C22⋊C4C2×D11semidirect
196. C24D44semidirect
227. C11#2613semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C23×C22⋊D112
C2×#670062
C2×#669392
C2×#669352
C11×#3792
#106225742
#106225732
#106225682
#106225562
#261311